You are given two jugs, a 4-gallon one and a 3-gallon one. Neither has any measuring marker on it. There is a tap that can be used to fill the jugs with water. How can you get exactly 2 gallons of water into the 4-gallon jug?

Use Breadth -First search i.e. finish expanding each row before going to the next one. It means expanding the {4,0} followed by the {0,3} states before going to their successors on the next row.

 

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